Key to Davies' Bourdon: With Many Additional Examples, Illustrating the Algebraic Analysis; Also, a Solution of All the Difficult Examples in Davies' LegendreA.S. Barnes & Company, 1856 - 205 من الصفحات |
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adding arithmetical progression cask cent clearing of fractions co-efficient combining and eliminating denote the number denote the quantity difference digits dividing both members equal equation whose roots expressed extracting the square factor find the values find x formula fractions and reducing given equation greatest common divisor hence inscribed circle Let ABC Let ACB Let x denote member from member member to member members and reducing Multiplying both members number of days number of dollars number of miles number of pounds number of shillings performing indicated operations perpendicular problem Prop quan real roots right-angled triangle rule SIMULTANEOUS EQUATIONS solution square root squaring both members substituting this value subtracting taking the upper three numbers transposing and reducing travelled upper sign variations whence X₁
مقاطع مشهورة
الصفحة 188 - IN a Triangle, having given the Base, the Sum of the other two Sides, and the Length of a Line drawn from the Vertical Angle to the Middle of the Base ; to find the Sides of the Triangle.
الصفحة 201 - To determine a Triangle ; having given the Lengths of three Lines drawn from the three Angles, to the Middle of the opposite Sides.
الصفحة 91 - What two numbers are those whose sum, multiplied by the greater, is equal to 77 ; and whose difference, multiplied by the lesser, is equal to 12 ? Ans.
الصفحة 92 - It is required to divide the number 24 into two such parts, that their product may be equal to 35 times their difference. Ans. 10 and 14.
الصفحة 74 - A company at a tavern had <£8 15s. to pay for their reckoning; but, before the bill was settled, two of them left the room, and then those who remained had 10s. apiece more to pay than before. How many were there in company ? Ans.
الصفحة 46 - A person has two horses, and a saddle worth £50 ; now, if the saddle be put on the back of the first horse, it will make his value double that of the second ; but if it be put on the back of the second, it will make his value triple that of the first ; what is the value of each horse ? Ans.
الصفحة 72 - What number is that, which, being divided by the product of its digits, the quotient is 3 ; and if 18 be added to it, the digits will be inverted ? Ans.
الصفحة 37 - Two persons, A and B, lay out equal sums of money in trade ; A gains $126, and B loses $87, and A's money is now double of B's : what did each lay out ? Ans. $300.
الصفحة 49 - A man and his wife usually drank out a cask of beer in 12 days ; but when the man was from home, it lasted the woman 30 days ; how many days would the man alone be in drinking it ? Ans.
الصفحة 187 - In a triangle, having given the ratio of the two sides, together with both the segments of the base made by a perpendicular from the vertical angle ; to determine the triangle.